DPS
Damage per Second Damage per Second, also known as DPS, is a measure of the average amount of damage a weapon will do over the course of continuous fire, taking into account delay between attacks, reload speed (if applicable), amount of ammo (if applicable), and damage per hit (before mitigation.) Weapons have the following four attributes that are used in the formula: Damage, Ammo, Delay, and Reload. Ranged weapons The following is the general formula of DPS used by ranged weapons suck as Rifles and Pistols: DPS = Damage × Ammo Delay × (Ammo - 1) + Reload Crossbows (and other single shot weapons) For Crossbows and other weapons that may only fire once before reloading: DPS = Damage Reload Melee weapons Melee Weapons use a similar formula as crossbows, but use Delay instead of Reload. DPS = Damage Delay Derivation General Formula As stated above, the four values that go into calculating DPS is the Damage, Ammo, Delay, and Reload value. Since DPS is defined as the average damage over continuous fire, and continuous fire is periodic, we can be break down continuous fire into periods of firing the weapons entire magazine and a reload period. Using just one magazine, we can derive the general formula for DPS by calculating the total amount of damage produced divided by the total amount of delay accrued. DPS = Total Damage Produced Total Delay Accrued First, we need the total amount of damage produced. Since each round does (on average) the amount of damage listed in the weapon's information, our total damage is simply the number of rounds in our magazine multiplied by the average damage per round. Total Damage Produced = Damage × Ammo For calculating the total delay accrued, we must consider what our Delay statistic means. Delay is the waiting period after firing a round before a weapon is ready to fire the next round. Every round in the magazine adds the Delay after being fired except the last one. Since there are no more rounds, there is no Delay before we enter the Reload period. As such, our formula for total accrued delay is as follows: Total Delay Accrued = Total Delay Between Shots + Reload Total Delay Between Shots = Delay × (Ammo - 1) Total Delay Accrued = Delay × (Ammo - 1) + Reload All together, we have the following general formula: DPS = Damage × Ammo Delay × (Ammo - 1) + Reload Single Shot Weapons In the case of single shot weapons, many of them list only either a Delay or a Reload. Since, as stated above, Delay is defined as the time between rounds, our Delay statistic is irrelevant, and in the case where a weapon lists only a Delay without a Reload, we will treat the weapon as having a Reload value equal to its Delay. Given the above, our previous general formula, using an Ammo of 1 and having our Delay and Reload statistics treated as equal, our new formula simplifies to the following: DPS = Damage × Ammo Delay × (Ammo - 1) + Reload = Damage × Ammo Reload × (Ammo - 1) + Reload = Damage × 1 Reload × (1 - 1) + Reload = Damage Reload Melee Weapons A melee weapon has no Reload and has no Ammo, so the general formula doesn't apply in the strictest sense. However, and while the formula listed for melee weapons should be self-evident, we can apply the general formula if we treat melee weapons in a special way. Instead of treating melee weapons as never having to reload, let's instead treat them as weapons that have an infinite amount of ammo before it must reload. Using the proposed definition of a melee weapon, our formula now looks like such: DPS = lim Ammo→∞ Damage × Ammo Delay × (Ammo - 1) + Reload Which, through the following reductions, we can show results in the above formula for Melee weapons: lim Ammo→∞ Damage × Ammo Delay × (Ammo - 1) + Reload = First, we rewrite the equation by pulling out Ammo from both sides. Notice that if we multiplied Ammo back into the quantity in the denominator, that would put us right back where we began. lim Ammo→∞ Ammo × Damage Ammo × ( Delay × (Ammo - 1) Ammo + Reload Ammo ) = Second, we expand the product in the denominator, more for clarity than anything else. lim Ammo→∞ Ammo × Damage Ammo × ( Delay × Ammo - Delay Ammo + Reload Ammo ) = Third, we cancel out the Ammo variable in the numerator and denominator. In this step, we also separate and simplify the fraction in the denominator. lim Ammo→∞ Damage Delay - Delay Ammo + Reload Ammo = Fourth, we apply our limit. While technically we can't divide by infinity anymore than we can divide by zero, for the sake of explanation, we'll overlook that. Damage Delay - Delay ∞ + Reload ∞ = Fifth, since any fixed value (e.g. Delay and Reload) taken over a value approaching infinity (i.e. Ammo) reduces to zero, we simplify our terms as such. Damage Delay - 0 + 0 = A final round of simplification leaves us with the equation provided in the section regarding Melee weapons. Damage Delay = DPS Category:Main Category